The killer was named locally last night as 20-year-old Adam Lanza, though police refused to confirm the identity.

Connecticut Police Lieutenant Paul Vance said the school shootings took place in one section of the buildings, in two rooms. He added: “There were 18 children who were pronounced dead at the school.

“There were two that were transported to area hospitals and pronounced dead. And there were six adults pronounced dead at the scene, at the school.

“The shooter is deceased in the school. There’s a great deal of work going on relative to that. That is the reason why we have not identified him as of yet.”

He went on: “It is not a simplistic scene – we need to establish identity, we need to document the entire scene and we need to answer every single question surrounding exactly how and why this incident occurred.

Answering questions, he said there was a “secondary crime scene” in Newtown, believed to be where the body of Lanza’s

father had been found.

Lt Vance added that New Jersey Police were assisting their Connecticut counterparts.

It was reported that Lanza drove up to the school and entered the building unchallenged, wearing a bullet-proof vest. His first victims were said to be the school’s principal and its psychologist, who were shot dead, and the vice-principal who was wounded.

Witnesses report that he was armed with two pistols and that the killings were focused around where his mother, named locally as Nancy, was teaching in the kindergarten area. They said he appeared to fire hundreds of rounds.

Parent Robert Licata said his six-year-old son was in class when the gunman burst in and shot the teacher: “That’s when my son grabbed a bunch of his friends and ran out the door. He was very brave. He waited for his friends.”

Mr Licata said the gunman did not speak during the attack.

Another parent said that Lanza had attempted to enter a music class, screaming “Let me in! Let me in!” and banging repeatedly on the door, but the teacher would not let him in.

Mergim Bajraliu, 17, heard the gunshots echo from his home and raced to check on his nine-year-old sister at the school.

He said his sister, who was fine, heard a scream come over the intercom at one point. He said teachers were shaking and crying as they came out of the building.

Police found two pistols, a Glock and a Sig Sauer, and a 0.223-calibre rifle at the scene.

Police officials were understood to be questioning the killer’s 24-year-old brother, Ryan, last night, though it is understood that authorities did not believe he was involved in the crime. Meanwhile, Lanza’s girlfriend and another friend were said to be missing in New Jersey.

Last night, an emotional President Barack Obama struggled to speak as he paid his respects to the dead, saying “there is not a parent in US who does not feel the same overwhelming grief as I do”.

He added: “We have to take meaningful action to prevent more tragedies, regardless of politics.”

At times using an index finger to wipe the corners of his eyes, Mr Obama paused repeatedly as he struggled to keep his composure while speaking of the children – aged between five and ten – who were killed. “Our hearts are broken,” he said.

The president ordered that US flags be flown at half-mast on public grounds until Tuesday.

Parents spoke of their shock at the massacre in the small community, one of the wealthiest counties in the country.

One parent said he had thought was “one of the safest places in America”.

A young child told American television he had seen and heard bullets before he was pulled into a classroom by a teacher. His mother said she believed the teacher had saved his life.

Another parent, Brenda Lebinski, who rushed to the school where her daughter is in the third grade, said: “Everyone was in hysterics – parents, students. There were kids coming out of the school bloodied. I don’t know if they were shot, but they were bloodied.”

She said a mother who was at the school during the shooting told her a “masked man” entered the principal’s office and may have shot the principal.

Ms Lebinski’s daughter’s teacher “immediately locked the door to the classroom and put all the kids in the corner of the room”.

Photographs from the scene showed children being escorted through a car park by adults, with their hands on each other’s shoulders.

Richard Wilford told reporters his seven-year-old son, Richie, said he heard a noise that “sounded like what he described as cans falling”.

The boy told him a teacher went out to check on the noise, came back in, locked the door and had the kids huddle up in the corner until police arrived. “There’s no words,” Wilford said. “It’s sheer terror, a sense of imminent danger, to get to your child and protect him.”

Melissa Makris said her ten-year-old son, Philip, saw what looked like a body under a blanket as he fled the school.

Last night, Prime Minister David Cameron issued a statement, saying: “My thoughts are with the injured and those who have lost loved ones.

“It is heartbreaking to think of those who have had their children robbed from them at such a young age, when they had so much life ahead of them.”

The Queen also sent her a message to Mr Obama in which she said she was “deeply shocked and saddened” to hear of the shootings.

Connecticut is known to have some of the toughest gun laws in the US, but critics say that it is easy for people bring guns in from another state without being detected.

The massacre is one of a number of deadly shootings in the United States this year.

In August, six people were killed at a Sikh temple in Wisconsin by a gunman, who was then shot dead by police.

In July, James Holmes was arrested by police in Colorado after a masked gunman opened fire at a midnight screening of Batman film The Dark Knight Rises, killing 12 and injuring a further 58. Holmes is currently awaiting trial.

Just this week, in Oregon, a gunman opened fire at a shopping mall, killing two people and then himself.

Last year, a gunman opened fire outside a shop in Tucson, Arizona, killing six people.